Question

10) Verify associativity property for multiplication of integers:

a) a= -5, b= 9, c=5

b) a= -13, b=9, c=3

c) a= 12, b=-4, c=2

d) a=0, b=-2, c=3

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Answer 1

a) a x (b x c) = (a x b) x c
= (-5) x (9 x 5) = (-5 x 9) x 5
= (-5) x 45 = (-45) x 5
= (-225) = (-225)

Hence verified

b) (-13) x (9 x 3) = (-13 x 9) x 3
= (-13) x 27 = (-117) x 3
= (-351) = (-351)

Hence verified

c) 12 x (-4 x 2) = (12 x -4) x 2
= 12 x (-8) = (-48) x 2
= (-96) = (-96)

Hence verified

d) 0 x (-2 x 3) = (0 x -2) x 3
= 0 x (-6) = (0) x 3
= 0 = 0

Hence verified

Answer 2

Answer:

Step-by-step explanation:

Associative property for multiplication of integers is given by

a×(b×c) = (a×b)×c, for any three integers a,b, and c

a) a= -5, b= 9, c=5

(b×c) = (9×5)  = 45

a×(b×c) = -5×45 = -225

(a×b) = -5×9 = -45

(a×b)×c = -45 ×5 = -225

Hence a×(b×c) = (a×b)×c is verified

b) a= -13, b= 9, c=3

(b×c) = (9×3)  = 27

a×(b×c) = -13×27 = -351

(a×b) = -13×9 = -117

(a×b)×c = -117 ×3 = -351

Hence a×(b×c) = (a×b)×c is  verified

c) a= 12, b= -4, c=2

(b×c) = (-4×2)  = -8

a×(b×c) = 12×-8 = -96

(a×b) = 12×-4 = -48

(a×b)×c = -48 ×2 = -96

Hence a×(b×c) = (a×b)×c is  verified

d) a= 0, b= -2, c=3

(b×c) = (-2×3)  = -6

a×(b×c) = 0×-6 = 0

(a×b) = 0×-2 = 0

(a×b)×c = 0 ×3 = 0

Hence a×(b×c) = (a×b)×c is verified

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